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35

Here is a free body diagram of the balls: … and one of the water volume: The four balance equations are $$ \begin{align} B_1 - T_1 - m_1 g & =0 \\ B_2 + T_2 - m_2 g & = 0 \\ F_1 + T_1 - B_1 - M g & = 0 \\ F_2 - B_2 - M g & = 0 \end{align} $$ where $\color{magenta}{B_1}$,$\color{magenta}{B_2}$ are the buoyancy forces, ...


34

This is a great question. An influential early discussion of it was given in a 1959 talk by Richard Feynman, There's Plenty of Room at the Bottom. Basically the answer is no, machines are not linearly scalable. For example, lubrication doesn't work for very small machines. A general way of looking at this is that we have various physical quantities, and they ...


20

The weight on the left bowl would be the weight of the water plus vase plus ping-pong ball (plus thread, ignored). The weight on the right bowl would be the weight of the water plus vase plus the buoyancy of the steel ball (plus the buoyancy of the submerged thread, ignored). That buoyancy is the weight of an equivalent volume of water. Since the ping-pong ...


18

A Thought Experiment We can arrive at an intuitive explanation without any special knowledge of physics. The strategy is to re-create the setup as closely as possible while keeping the two sides in balance. Imagine that you start with two identical beakers, filled with the same amount of water, no balls. Placed on the scale, they balance. On the left, ...


7

Instead of assuming the earth is made of metallic hydrogen, let's just compare Earth's density of $5.52 \times 10^3 kg/m^3$ to that of neutrons' $2.3 \times 10^{17} kg/m^3$ because degenerate matter consisting of neutrons is what you get when electrons are forced into nuclei. That's a density increase of about $4.17 \times 10^{13}$ (at least 3 orders of ...


6

When you look at crystalline substances, there is really not that much space between the atoms. What people mean when they say that an atom is mostly empty space, is that the INSIDE of the atom is very sparsely populated with stuff. This is because the stuff in question, the nucleus and the electrons, are tiny in comparison to the actual size of the atom. ...


4

Reynold's number is defined to be: $$ \text{Re} = \frac{ v D }{ \nu } $$ where $v$ is the characteristic velocity for the flow, $D$ is a characteristic size and $\nu$ is the kinematic viscosity. Now, why should we care? Why is Reynold's number important? Well, the first thing to realize is that the Reynolds number is a dimensionless number. This means ...


3

I'm amazed that this is so confounding to some. This is too long to be a comment, so I'm making it an answer. The TL;DR version: The answers that say the scale will tilt down to the right are correct. The beaker full of water with the steel ball suspended from above is heavier than is the beaker that contains the ping pong ball anchored from below. ...


3

According to the same Wikipedia article you cite, ...the zero point is determined by placing the thermometer in brine: he used a mixture of ice, water, and ammonium chloride, a salt, at a 1:1:1 ratio. This is a frigorific mixture which stabilizes its temperature automatically: that stable temperature was defined as 0 °F (−17.78 °C). The second point, at ...


3

Actually, the Higgs scale is not the TeV scale. The Higgs scale is the scale of electroweak symmetry breaking, i.e. $\mathcal O(100 \mathrm{GeV})$. The Terascale comes into play along with the Higgs, as supersymetry - the most popular extensions of the Standard Model - would actually like a small Higgs mass, much smaller than its measured value ($< M_Z$ ...


2

If you want the new physics to solve the hierarchy problem, it's best if it is close to the weak scale, or else you will be left with a residual little hierarchy. You are describing the "big desert" between the weak and GUT scales. I think it was motivated by the idea that SUSY lived at the weak scale, solving the hierarchy problem and insuring gauge ...


2

As already said size of elementary particles is not so simple. Orderer from high mass to lower (add 125GeV to the Higgs): (From Matt Strassler's blog) Anyway, why don't you create an image yourself?


2

The story is this, as much as I remember. Fahrenheit chose the zero point on his scale as the temperature of a bath of ice melting in a solution of common table salt (a routine 18th century way of getting a low temperature). He set $32^{\circ}$ as the temperature of ice melting in water. For a reproducible high point on the scale he chose the temperature of ...


2

Well I got this badly wrong, and grovellingly apologise to those I traduced. It seemed easy: the water in both is the same weight, so I thought that removing it would make no difference to the balance. This was wrong: removing the water from the right hand beaker does have an effect, the presence of the suspended ball does add extra weight to it, so the ...


2

The elasticity does not influence the measurement as long as the scale stands perfectly level and you stand perfectly still. The angle of the floor however can greatly influence the result. Your gravitational force won't compress the spring in full strength, it will rather split into normal force and downhill force. The spring will only "see" the normal ...


1

At first you'd burn your hand, then it would feel like a normal rock. An orange sized Earth would cool very rapidly. If an object gets twice as big, its volume increases by $2^3$, but its surface increases only by $2^2$. You can only lose heat at the surface but you 'hold' all your heat in your interior. Simply said, the bigger something is, the harder it ...



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